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5G and beyond wireless networks are the upcoming evolution for the current cellular networks to provide the essential requirement of future demands such as high data rate, low energy consumption, and low latency to provide seamless communication for the emerging applications. Heterogeneous cloud radio access network (H-CRAN) is envisioned as a new trend of 5G that uses the advantages of heterogeneous and cloud radio access networks to enhance both the spectral and energy efficiency. In this paper, building on the notion of effective capacity (EC), we propose a framework in non-orthogonal multiple access (NOMA)-based H-CRAN to meet these demands simultaneously. Our proposed approach is to maximize the effective energy efficiency (EEE) while considering spectrum and power cooperation between macro base station (MBS) and radio remote heads (RRHs). To solve the formulated problem and to make it more tractable, we transform the original problem into an equivalent subtractive form via Dinkelbach algorithm. Afterwards, the combinational framework of distributed stable matching and successive convex algorithm (SCA) is then adopted to obtain the solution of the equivalent problem. Hereby, we propose an efficient resource allocation scheme to maximize energy efficiency while maintaining the delay quality of service (QoS) requirements for the all users. The simulation results show that the proposed algorithm can provide a non-trivial trade-off between delay and energy efficiency in NOMA H-CRAN systems in terms of EC and EEE and the spectrum and power cooperation improves EEE of the proposed network. Moreover, our proposed solution complexity is much lower than the optimal solution and it suffers a very limited gap compared to the optimal method.